Abe challenges Bee to determine a

*3-digit positive integer* N.

It is known that the

*number formed by the last two digits of N* when divided by 9, yields a remainder of 3.

Abe makes the following statements, precisely one of which is false:

- N divided separately by each of 2, 4, 6, and 8 yields a remainder of 1.
- N divided separately by each of 5 and 7 yields a remainder of 2.
- N divided separately by each of 5 and 11 yields a remainder of 3.

Determine the value of N from the above statements and given clues.

Just looking at the problem on the board perceived that the last two digits must be 21+18k i.e 21,39,57,75 and 93.

Looking at the last digit mod 5 only **57** and **93** remained.

checking for hundreds:

457 and 993 both qualify

The statement "Abe makes the following statements, **precisely** one of which is false:" is a false statement.